Citation Formats

Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, and Rabitz, Herschel. Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.95.063418.

Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, & Rabitz, Herschel. Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape. United States. doi:10.1103/PhysRevA.95.063418.

Riviello, Gregory, Wu, Re-Bing, Sun, Qiuyang, and Rabitz, Herschel. Thu .
"Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape". United States. doi:10.1103/PhysRevA.95.063418.

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, butmore » certain control constraints can still prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.« less